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A very simple procedure to extract pseudopotentials from ab initio atomic calculations is presented. The pseudopotentials yield exact eigenvalues and nodeless eigenfunctions which agree with atoxnic wave functions beyond a chosen radius x,. Moreover, logarithmic derivatives of real and pseudo wave functions and their first energy derivatives agree for r &r, guaranteeing excellent transferability of the pseudopotentials. Pseudopotentials were originally introduced to simplify electronic structure calculations by eliminating the need to include atomic core states and the strong potentials responsible for binding them. ' Two roughly distinct lines of recent development are discernable: In one, ion pseudopotentials of enforced smoothness were empirically fitted to reproduce experimental energy bands. ' Consequently, wave functions were only approximately described. In the other, the orthogonalized-plane-wave (OPW) concept underlying the pseudopotential method was used to derive "first principles" pseudopotentials from atomic calculations. ' These latter potentials are generally "hard core" in character, that is, strongly repulsive at the origin. The resulting wave functions generally exhibit the correct shape outside the core region; however, they differ from the real wave functions by a normalization factor. 'It is the purpose of this Letter to demonstrate that the normalization and hard-core problems can be solved simultaneously, while also maximizing the range of systems in which a pseudopotential gives accurate results.The new family of energy-independent pseudopotentials introduced here have the following desirable properties:(1) Real and pseudo valence eigenvalues agree for a chosen "prototype" atomic configuration.(2) Real and pseudo atomic wave functions agree beyond a chosen "core radius" r,.(3) The integrals from 0 to r of the real and pseudo charge densities agree for r &r, for each valence state (norm conservation).(4) The logarithmic derivatives of the real and pseudo wave function and their first energy deriv atives agree for r &r,.Properties (3) and (4) are crucial for the pseudopotential to have optimum transferability among a variety of chemical environments in self-consistent calculations in which the pseudo charge density is treated as a real physical object. 'This approach starids in contrast to earlier OPW-like approaches" ' in which the normalized pseudo wave functions have to be orthogonalized to core states and renormalized in order to yield accurate charge densities outside the core region. ' Property (3) guarantees, through Gauss's theorem, that the electrostatic potential produced outside r, is identical for real and pseudo charge distributions. Property (4) guarantees that the scattering properties of the real ion cores are reproduced Mlitk rnininzum error as bonding or banding shifts eigenenergies away from the atomic levels. A central point of our approach is that these two aspects of transferability are related by a simple identity. The method permits the potentials to be intrinsically ...

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A theory is presented for vacuum tunneling between a real solid surface and a model probe with a locally spherical tip, applicable to the recently developed "scanning tunneling microscope. " Calculations for 2&& 1 and 3& 1 reconstructions of Au(110) are in excellent agreement with recent experimental results, if an effective radius of curvature of 9 g is assumed for the tip.

Fully-nonlocal two-projector norm-conserving pseudopotentials are shown to be compatible with a systematic approach to the optimization of convergence with the size of the plane-wave basis. A new formulation of the optimization is developed, including the ability to apply it to positive-energy atomic scattering states, and to enforce greater continuity in the pseudopotential. The generalization of norm-conservation to multiple projectors is reviewed and recast for the present purposes. Comparisons among the results of all-electron and one-and two-projector norm-conserving pseudopotential calculations of lattice constants and bulk moduli are made for a group of solids chosen to represent a variety of types of bonding and a sampling of the periodic table.2